otf connect webinar - connecting the 4-part math lesson to number sense and algebra
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4-Part Math Lesson:Number Sense & Algebra
@MathletePearce
tapintoteenminds.com
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Last Time…
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Two Groups of Students
Good at Math
Not Good at Math
Struggle withunfamiliarproblems
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Two Groups of Students
Good at Memorization
Not Good at Memorization
Struggle withunfamiliarproblems
TEST QUESTION
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TEST QUESTION
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=EXAMPLE
TEST QUESTION
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=HOMEWORK
TEST QUESTION
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=TEXTBOOK
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UNFAIR
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Two Groups of Students
Good atMath
NotGood at
Math
@MathletePearcewww.tapintoteenminds.com
Two Groups of Students
Good at Memorization
Not Good at Memorization
Good at Memorization
Not Good at Memorization
Struggle withunfamiliarproblems
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Two Groups of Students
UNFAIR
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New Knowledge
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New Knowledge
Prior Knowledge
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MATH
SILO1
SILO2
SILO3
SILO4
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MATHSILO
1SILO
2SILO
3SILO
4
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MATHSILO
1SILO
2SILO
3SILO
4
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A VISION FOR MATHEMATICS
EDUCATION
VISION
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Contextual
VISION
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Visual and ConcreteContextual
VISION
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Interconnected
Visual and ConcreteContextual
VISION
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Interconnected
Visual and ConcreteContextual
CONFIDENCE
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Interconnected
Visual and ConcreteContextual
PERCEPTION
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Interconnected
Visual and ConcreteContextual
STUDENT SUCCESS
Connections
Minds On
Consolidate
Inquiry1.
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2.
3. 4.
-Part Math Lesson4
Connections
Minds On
Consolidate
Inquiry
1.
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2.
3.
4.
-Part Math Lesson4
Interconnected
Visual and Concrete
Contextual
VISION
Connections
Consolidate
Inquiry
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2.
3.
4.
Interconnected
Visual and ConcreteContextual
VISION
MINDS ON -Part Math Lesson4
Consolidate
Inquiry
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2.
4.
Connect to New Learning Goal
Visual and ConcreteContextual
VISION
MINDS ON
CONNECTIONS
-Part Math Lesson4
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Visual and ConcreteContextual
VISION
MINDS ON
INQUIRY
CONNECTIONS
-Part Math Lesson
Consolidate4.4
Prior Knowledge & Intuition
Connect to New Learning Goal
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Visual and ConcreteContextual
VISION
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
Apply New Skill Through Practice
@MathletePearcewww.tapintoteenminds.com
Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
4-PartLesson
Apply New Skill Through Practice
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Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
4-PartLesson:Apply New Skill
Through Practice Number Sense & Algebra
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Number Sense & Numeration
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Number Sense & Numeration
Grade 9 Academic
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Number Sense & Numeration
Grade 9 Applied
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Algebra
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Algebra
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Algebra
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Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
Apply New Skill Through Practice
4-PartLesson:
Number Sense & Algebra
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“Chunk” Into Friendly Numbers
multipl
y
129 x3
3 3 3 2
3
3
10
9
12
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Multiplication Chunking Model
multipl
y
3
3 3 3 2
3
3
10
9
9 (10 + 2)
10
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Multiplication Chunking Model
multipl
y
3
2
3
3
9
9=9(10 + 2 )
(10)
10
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Multiplication Chunking Model
multipl
y
3
2
3
3
9
9 (10 + 2 )9= (10) 9(2)+
10
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Multiplication Chunking Model
multipl
y
3
2
3
3
9
9 (10 + 2 )9= (10) 9(2)+
10
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Multiplication Chunking Model
multipl
y
3
2
3
3
9
9 (10 + 2 )9= (10) 9(2)+90=90
10
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Multiplication Chunking Model
multipl
y
3
2
3
3
9
9 (10 + 2 )9= (10) 9(2)+90=90 18+18
10
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Multiplication Chunking Model
multipl
y
3
2
3
3
9
9 (10 + 2 )9= (10) 9(2)+90=90 18+18
= 108108
10
3
multipl
y
510
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1513 x15
13
13
multipl
y
510
13
15
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510
(10 + 5)
1513 x
=
510
10
3
multipl
y
510
13
13
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1513 x
=
( 10 + 5 )=
3
(10 + 3 )
( 10 + 5 )10
5
3
10
3
multipl
y
510
13
15
13
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10 1513 x
=
( 10 + 5 )= (10 + 3 )
( 10 + 5 )10
5
3
10
3
multipl
y
510
13
15
13
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10 1513 x
=
( 10 + 5 )=10
(10 + 3 )
( 10 + 5 )
= 100
100
3
10
10
3
multipl
y
510
13
13
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5 1513 x
=
( 10 + 5 )=10
(10 + 3 )
( 10 + 5 )
= 100
100
10
3
10
3
multipl
y
510
13
13
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5 1513 x
=
( 10 + 5 )=10
(10 + 3 )
( 10 + 5 )
= 100
100
+ 50
50
10
10
3
multipl
y
510
13
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5 1513 x
=
( 10 + 5 )=
3
(10 + 3 )
( 10 + 5 )
= 100
100
+ 50
50
10
1010
3
multipl
y
510
13
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5 1513 x
=
( 10 + 5 )=
3
(10 + 3 )
( 10 + 5 )
= 100
100
+ 50
50
30+ 30
10
1010
3
multipl
y
510
13
@MathletePearcewww.tapintoteenminds.com
5 1513 x
=
( 10 + 5 )=
3
(10 + 3 )
( 10 + 5 )
= 100
100
+ 50
50
30+ 30
10
1010
3
multipl
y
510
13
@MathletePearcewww.tapintoteenminds.com
5 1513 x
=
( 10 + 5 )=
3
(10 + 3 )
( 10 + 5 )
= 100
100
+ 50
50
30+ 30 + 15
15
10
3
multipl
y
510
13
15
13
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510 1513 x
=
( 10 + 5 )=10
3
(10 + 3 )
( 10 + 5 )
= 100
100
+ 50
50
30+ 30 + 15
15= 195
195
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Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
Apply New Skill Through Practice
4-PartLesson:
Number Sense & Algebra
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Introducing Distribution With Unknowns
146( )( )
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146( )( )mult
iply
146
Introducing Distribution With Unknowns
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146( )( )mult
iply
146
Introducing Distribution With Unknowns
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146( )( )mult
iply
6
14
Introducing Distribution With Unknowns
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146( )( )10 + 4mult
iply
6
14
Introducing Distribution With Unknowns
+x
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16( )( )x 4mult
iply
64
Introducing Distribution With Unknowns
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multipl
y
6
14x 4
+x16( )( )x 44
Introducing Distribution With Unknowns
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multipl
y
6
14x 4
+x16( )( )x 44
Introducing Distribution With Unknowns
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multipl
y
6
14x 4
+x16( )( )x 44
Introducing Distribution With Unknowns
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6( )( )x + 4mult
iply
6
14x 4
6 x( )( )= 6 x( )( )=6
x
Introducing Distribution With Unknowns
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multipl
y
6
4
610=6x
1066x
14xx
6( )( )x + 4
6 x( )( )= 6 x( )( )=
Introducing Distribution With Unknowns
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4multipl
y
6 1066x
14xx
610=6x
6( )( )x + 4
6 x( )( )= 6 x( )( )=
Introducing Distribution With Unknowns
6x
x
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4multipl
y
6 1066x
x
=
6( )( )x + 4
6 x( )( )= 6 x( )( )=
Introducing Distribution With Unknowns
6x
x
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4multipl
y
6 1066x
x
=
6( )( )x + 4
6 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )4
Introducing Distribution With Unknowns
6x
x
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4multipl
y
6 1066x
x
=
6( )( )x + 4
6 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )464+24
6424
Introducing Distribution With Unknowns
6x
x
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4multipl
y
6 1066x
x
=
6( )( )x + 4
6 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )464+24
6424
Introducing Distribution With Unknowns
6x
x
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4multipl
y
6 1066x
x
=
6( )( )x + 4
6 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )464+24
6424
Introducing Distribution With Unknowns
6x
x
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4multipl
y
6 1066x
x
=
6( )( )x + 46 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )4
64+24
6424 =6( )( )14
Introducing Distribution With Unknowns
60
10
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4multipl
y
6 10660
=
6( )( )10 + 46 x( )( )= 6 10( )( )= 6( )( )4+ 6( )( )4
64+ 24
6424=
6( )( )14
Introducing Distribution With Unknowns
60
10
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4multipl
y
6 10660
=
6( )( )10 + 46 x( )( )= 6 10( )( )= 6( )( )4+ 6( )( )4
64+ 24
6424=
6( )( )14
84=
84
Introducing Distribution With Unknowns
6xx
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Digging Deeper
5( )( )+ 6multipl
y
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The Distributive Property
multipl
y
6xx5( )( )+ 611111
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The Distributive Property
multipl
y
6xx5( )( )+ 6x
11111
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The Distributive Property
multipl
y
6xx5( )( )+ 61x 1 1 1 1 1
11111
5
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The Distributive Property
multipl
y
6xx5( )( )+ 61x 1 1 1 1 1
11111
5( )( )
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )= x5( )( )=
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=x5( )( )=
xxxxx
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=x5=
xxxxx
5( )( )6
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=x5=
xxxxx
5( )( )6
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=x5=
xxxxx
5( )( )6+ 5( )( )6
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=x5=
xxxxx
5( )( )6+5( )( )6+ 30
1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1
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The Distributive Property
multipl
y
6xx
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=x5=
xxxxx
5( )( )6++ 30
1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1
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Extending to Solving Equations
multipl
y
6x
x
5( )( )+ 61x 1 1 1 1 1
11111
5( )( )=
x5=
xxxxx
5( )( )6+
+ 30
1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1
= 85
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multipl
y
6x
x
5( )( )+ 61x 1 1 1 1 1
11111
5( )( ) =
x5 =
xxxxx
5( )( )6+
+ 30
1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1
= 85
85
85
Extending to Solving Equations
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Digging Deeper
x + 59( )Find the missing “magic number”
= 99
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Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
Apply New Skill Through Practice
Area, Perimeter, & Volume
23x3x 2
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2nd Degree Polynomials
2x( )( )+multipl
y
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multipl
y
23x3x 22x( )( )+x
x
x x x 1 1
x
x
x x x
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multipl
y
23x3x 22x( )( )+x
x
x x x 1 1
x
x
x x x
2x( )( )
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multipl
y
23x3x
22x( )( )+x
x
x x x 1 1
x
x
x x x
)2x( )( )=
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multipl
y
23x3x 22x( )( )+x
x
x x x 1 1
x2x
x
x
x x
x2 x2
x2 x2 x2
3x2x( )( )= 6x23x2x( )( )=
6x
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multipl
y
23x3x 22x( )( )+x
x
x x x 1 1
x
x
x x
x x
x x x=
3x2x( )( )=
2x( )( )+
6x
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multipl
y
23x3x2
2x( )( )+x
x
x x x 1 1
x
x
x x
x x
x x x=
3x2x( )( )= 2x( )( )++x
xx
x
xx
6x
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multipl
y
23x3x2
2x( )( )+x
x
x x x 1 1
x
x
x x
x x
x x x=
3x2x( )( )= 2x( )( )++x
xx
x
xx
22x( )( )+ 4x
4x6x2
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multipl
y
23x3x2
2x( )( )+x
x
x x x 1 1
x2
x
x x
x2 x2
x2 x2 x2
=3x2x( )( )= 2x( )( )+
x
xx
x
xx
+6x2 4x
3x3x
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4x( )( )
2nd Degree Equations
Find the missing “magic number”
=300
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Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
Apply New Skill Through Practice
Area, Perimeter, & Volume
8x
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7x( )( )
2nd Degree Equations
Find the missing “magic number”
=2,744
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Visual and ConcreteContextual
MINDS ON
CONNECTIONS
INQUIRYCONSOLIDATEPrior Knowledge
& Intuition
Connect to New Learning Goal
Apply New Skill Through Practice
Area, Perimeter, & Volume
Task
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I’ve got a yard…So…
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… and I needI’ve got a yard…
… and I need
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What do we What is the … and I need
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a fence.
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What do we
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PERIMETER
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What is the perimeter…
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What is the perimeter…
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What is the perimeter…
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What is the perimeter…
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What is the perimeter…
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2 ft
What is the perimeter…
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2 ft 2 ft
What is the perimeter…
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What is the perimeter…
n+
24n
+2
4
nn1212
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What is the perimeter…
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
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P = l+ l +w+ w
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
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P = l+ l +w+ w
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
@MathletePearcewww.tapintoteenminds.com
P = ll +w+ w2
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
@MathletePearcewww.tapintoteenminds.com
P = ll +w+ w2
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
@MathletePearcewww.tapintoteenminds.com
P = ll + ww2
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
2
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P = ll + ww2
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212
2( )
ll@MathletePearcewww.tapintoteenminds.com
P = + ww2
n+
24n
+2
4
n
n12
12
n+
24n
+2
4
n
n
12
122( )
ll@MathletePearcewww.tapintoteenminds.com
P = + ww2
n+
24
n+24n
n12
12
n+
24
n+24
n
n
12
122( )
ll@MathletePearcewww.tapintoteenminds.com
P = +2
n+
24
n
n12
12
n+
24
n12
( )n+24
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
LIKE TERMS
llP = +2 n12( )n+24
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
LIKE TERMS
llP = +2 n12( )n+2416
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12( )n+2416ll +n12( )n+2416
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12( )n+2416ll +n12( )n+2416 ( )n+216+
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12( )n+2416ll +n12( )n+24162
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12( )n + 2416ll +n12 ()n + 2416 2
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12 )n + 2416ll +n12 (n + 2416 232
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12 )n + 2416ll +n12 (n + 2416 232
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12n + 2416ll +n12n + 2416 232 4
@MathletePearcewww.tapintoteenminds.com
n+
24
n12
n+
24
n12
llP = +2 n12n + 2416ll +n12n + 2416 232 4
@MathletePearcewww.tapintoteenminds.com
I also need…
fertilizer.
@MathletePearcewww.tapintoteenminds.com
I also need…
What do we
@MathletePearcewww.tapintoteenminds.com
fertilizer.
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
What do we
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
AREA
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
What is the area
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
n2
n
n
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
n2
n
n n2
n
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
n2
n
n n2
n
n2 n2 n2 n2 n2 n2
n2 n2 n2 n2 n2 n2 n2 n2
n2 n2 n2 n2 n2 n2 n2 n2
n2 n2 n2 n2 n2 n2 n2 n2
n2 n2 n2 n2
n2 n2 n2 n2
n2 n2 n2 n2
n2 n2 n2 n2
n n n n n n n n n n
n
n
n
@MathletePearcewww.tapintoteenminds.com
2 ft 2 ft
n2
n
n n2
n
n2 n2 n2 n2 n2 n2
n2 n2 n2 n2 n2 n2 n2 n2
n2 n2 n2 n2 n2 n2 n2 n2
n2 n2 n2 n2 n2 n2 n2 n2
n2 n2 n2 n2
n2 n2 n2 n2
n2 n2 n2 n2
n2 n2 n2 n2
n n n n n n n n n n
n
n
n
2n 2n 2n 2n 2n 2n 2n 2n 2n 2n 2n 2n
@MathletePearcewww.tapintoteenminds.com
n+
24n
+2
4 n+
24 n
+2
4
nn1212
nn1212
@MathletePearcewww.tapintoteenminds.com
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212A = lw
@MathletePearcewww.tapintoteenminds.com
n+
24n
+2
4
nn1212
n+
24n
+2
4
nn1212A = lw
@MathletePearcewww.tapintoteenminds.com
n+
24n
+2
4
n
n
12
12
n+
24n
+2
4
nn1212A = l w( )
@MathletePearcewww.tapintoteenminds.com
n+
24n
+2
4
n
n
12
12
n+
24n
+2
4
nn1212A = l w( )
n+24n12 n+ 24( )( )@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+ 24nn1212
A = l w( )( )
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+ 24nn1212
A = ( )( )n+24n12 n+ 24( )( )
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+ 24nn1212
A = w( )( )n12 n+ 24( )( )
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+ 24nn1212
A = w( )( ) n12 n+ 2 4( )( )= n12 n4( )( )
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+ 24nn1212
A = w( )( ) n12 n+ 2 4( )( )=
n12 n4( )( )
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+ 24nn1212
A = w( )( ) n12 n+ 2 4( )( )=
n12 n4( )( )
n+24n12 n+ 24 w( )( )+ 2
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12 n+ 4( )( )=
n12 n4( )( )
n+4 n12+w ( )( )+ 2n12( )( )2
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12 n+ 4( )( )=
n12 n4( )( )
n+4 n12+w ( )( )+ 2
n12( )( )2
+
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12 n+ 4( )( )=
n12 n4( )( )
n+4 +w+
n12( )( )2
n12( )( )2+
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12 n+ 4=
n12 n4
n+4 +w+
n12( )( )2
n12( )( )2+
48
48
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12n+ 4=
n12 n4
n+4 +w+
n12( )( )2
n12( )( )2+
48
48
n2
n2
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12n+ 4=
n12 n4
n+4 +w+
n12( )( )2
n12( )( )2+
48
48
n2
n2
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12n+ 4=
n12 n4
n+4 +w+
n122
n122+
48
48
n2
n2
24
24
@MathletePearcewww.tapintoteenminds.com
n+
24
n+24
n
n
12
12
n+
24
n+24nn1212
A = w( )( ) n12n+ 4=
n12 n4
n+4 +w+
n122
n122+
48
48
n2
n2
24
24
@MathletePearcewww.tapintoteenminds.com
If…
@MathletePearcewww.tapintoteenminds.com
fencing has a cost of
@MathletePearcewww.tapintoteenminds.com
fencing has a cost of$24.50 per foot…
@MathletePearcewww.tapintoteenminds.com
and
@MathletePearcewww.tapintoteenminds.com
fertilizer
@MathletePearcewww.tapintoteenminds.com
fertilizerhas a cost of
@MathletePearcewww.tapintoteenminds.com
@MathletePearcewww.tapintoteenminds.com
… and covers 1800 feet-squared
@MathletePearcewww.tapintoteenminds.com
$24.50 per foot…
How … and covers 1800 feet-squared
@MathletePearcewww.tapintoteenminds.com
$24.50 per foot…
covers 1800 feet-squared
How
5.25 feet
Your Turn…
@MathletePearcewww.tapintoteenminds.com
Your Turn…
@MathletePearcewww.tapintoteenminds.com
Think of an example involving number sense and algebra that
you could introduce using context and visuals.
Share…
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